Local Rings At Non-Closed Points

Algebraic Geometry
Post Reply
Tsakanikas Nickos
Community Team
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

Local Rings At Non-Closed Points

#1

Post by Tsakanikas Nickos »

Let $A$ be a ring, let $\mathfrak{p}$ be a prime ideal of $A$ and let $\mathfrak{m}$ be a maximal ideal of $A$ containing $\mathfrak{p}$. Show that $ A_{\mathfrak{p}} = \left( A_{\mathfrak{m}} \right)_{\mathfrak{p}A_{\mathfrak{m}}} $. Conclude that the local ring at a non-closed point (of a scheme) is the localization of a local ring at a closed point.
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 6 guests